As mentioned in the main text, Mg\(_{2}\) Si\(_{1-x}\) Sn\(_{x}\)  is a system whose \(n\) -type PF clearly benefits from alloying, peaking around \(x\sim 0.7\)  [1]}, [2]}, [3]}. It is presumed that the convergence of its two lowermost conduction bands is responsible for this enhancement, though it occurs at one point (the \(X\) -point). We confirm that this convergence occurs by calculating of alloy band structure at \(x=0.75\)  using HSE06 [4]}, [5]} hybrid functional and BandUP [6]}, [7]}, shown in Fig. REF . However, we cannot positively confirm here whether band convergence indeed is the (primary) reason because the alloys are metallic at the plain DFT level even with \(x\sim 0.5\) , and hence not amenable to an EPW study. That said, we find a few other reasons that could be primarily responsible for the peak PF around \(x\sim 0.7\) .
